Canonical models of arithmetic (1; e)-curves

Jeroen Sijsling (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

The Fuchsian groups of signature (1; e) are the simplest class of Fuchsian groups for which the calculation of the corresponding quotient of the upper half plane presents a challenge. This paper considers the finite list of arithmetic (1; e)-groups. We define canonical models for the associated quotients by relating these to genus 1 Shimura curves. These models are then calculated by applying results on the p-adic uniformization of Shimura curves and Hilbert modular forms.

Mots clés: Shimura curves; Arithmetic groups; Uniformization; Explicit methods

Domaines: Géométrie algébrique [math.AG]

Jeroen Sijsling. Canonical models of arithmetic (1; e)-curves. Mathematische Zeitschrift, 2013, 273 (1-2), pp.173-210. ⟨10.1007/s00209-012-1000-5⟩. ⟨hal-00831342⟩